Question

tan A + cot A = 2 then find the value of , tan^3 A + 7 cot ^ 3 A​

Answer 1

tan A + cot A = 2 -----(1)

But, we know that tan A × cot A = 1

So,

cot A = 1/tanA

Put in (1)

tan A + 1/tanA = 2

tan^2A + 1 = 2tanA

tan^2A - 2tanA + 1 = 0

tan^2A - tanA - tanA + 1 = 0

tan A (tanA - 1) - 1(tan A - 1) = 0

tan A = 1 or tan A = 1

So A = 45

Now,

tan^3A + 7cot^3A

= tan^3(45) + 7cot^3(45)

= (1)^3 + 7(1)^3

= 1 + 7

= 8